Lesson 28 · Eight-directional movement

Eight-directional movement

Real agents move diagonally, not just along the axes. Today you add the four diagonal neighbors in a fixed order, with a corner rule that forbids squeezing diagonally between two walls.

The goal

Enumerate eight-directional neighbors in a fixed order, forbidding diagonal moves through wall corners.

Start here - the target

TO DO

Scenario: Diagonal neighbors are added in order, blocked at wall corners

Givena 3 by 3 open grid and the eight-direction order N, E, S, W, NE, SE, SW, NW

WhenNeighbors8 of the center (1, 1) is requested

Thenit returns (1,0), (2,1), (1,2), (0,1), (2,0), (2,2), (0,2), (0,0) in that order

Andon a grid with a wall at (1, 0), Neighbors8 of (0, 0) returns only (0, 1): the diagonal to (1, 1) is forbidden because the corner cell (1, 0) is a wall

Background

Restricting movement to four directions makes paths blocky. Allowing the four diagonals too lets an agent cut across open space, which is how movement works in most games and robotics. We list the diagonals after the orthogonals so the fixed order still determines tie-broken paths, extending the same determinism to eight-way movement.

Diagonals bring one new rule. Sliding diagonally between two walls that meet at a corner would clip through solid geometry, so the corner rule forbids a diagonal step unless both orthogonal cells it passes beside are open. Moving from (0,0) to (1,1) requires (1,0) and (0,1) to both be walkable; wall off either and the diagonal is blocked even though the destination itself is open. Without this rule a path could ooze through a wall corner, which no physical agent can do. Next these diagonal steps get a cost, and a heuristic to match.

Make it work

// the four orthogonals first (same as dir4), then the four diagonals
var dir8 = []Coord{{0,-1},{1,0},{0,1},{-1,0}, {1,-1},{1,1},{-1,1},{-1,-1}}
func (g *Grid) Neighbors8(c Coord) []Coord {
  out := []Coord{}
  for _, d := range dir8 {
    n := Coord{c.X + d.X, c.Y + d.Y}
    if !g.Walkable(n) { continue }
    if d.X != 0 && d.Y != 0 { // diagonal: both shared orthogonal cells must be open
      if !g.Walkable(Coord{c.X + d.X, c.Y}) || !g.Walkable(Coord{c.X, c.Y + d.Y}) { continue }
    }
    out = append(out, n)
  }
  return out
}

CheckpointDONE

Cells report eight-directional neighbors with a corner rule. Commit and stop here.